Problem: What do the following two equations represent? $-5x+4y = -3$ $-25x+20y = 3$
Solution: Putting the first equation in $y = mx + b$ form gives: $-5x+4y = -3$ $4y = 5x-3$ $y = \dfrac{5}{4}x - \dfrac{3}{4}$ Putting the second equation in $y = mx + b$ form gives: $-25x+20y = 3$ $20y = 25x+3$ $y = \dfrac{5}{4}x + \dfrac{3}{20}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.